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What is improperness?

What is improperness? Here are some definitions.

Noun
  1. Quality of being improper.
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In this work, we investigate the effect of severe improperness of fitted binormal ROC curves on the reliability of AUC estimates when the data arise from an actually proper curve.
Hence the failure of the more restricted model may, or may not, be signaling the improperness of even a fitting Figure 1 style model.
He only knew about the improperness when the case was under the process of investigation.
It reminded of the many times that people had pointed out the improperness of my language.
Several choices of σ will be used to show how the advantages of WL processing vary with the level of improperness of the observations.

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